Put every study on the same vertical scale before comparing them

A forest plot draws each study at its own precision, so the eye compares intervals of different widths and cannot see heterogeneity. Dividing by the standard error puts every point on a unit-variance axis: under homogeneity the points scatter with unit standard deviation about a line through the origin, so a study more than two units off the line is visibly discrepant regardless of its size.

Usage

Magal(yi, se_i)

Arguments

yi

Study effect estimates.

se_i

Their standard errors, strictly positive.

Value

List with z, x, slope, resid, n_outside_2, k.

Details

Formula: z_i = y_i/se_i against x_i = 1/se_i; the through-the-origin slope sum(z_i x_i)/sum(x_i^2) is exactly the inverse-variance pooled estimate – Galbraith (1988).

References

Galbraith, R. F. (1988). Statistics in Medicine 7(8):889-894. doi:10.1002/sim.4780070807 .

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Magal(V, V)
#> $z
#> [1] 1 1 1 1 1 1 1 1
#> 
#> $x
#> [1] 1.0000000 0.5000000 0.3333333 0.2500000 0.2000000 0.1666667 0.1428571
#> [8] 0.1250000
#> 
#> $slope
#> [1] 1.779375
#> 
#> $resid
#> [1] -0.7793753  0.1103123  0.4068749  0.5551562  0.6441249  0.7034374  0.7458035
#> [8]  0.7775781
#> 
#> $n_outside_2
#> [1] 0
#> 
#> $k
#> [1] 8
#> 
#> $method
#> [1] "Galbraith (radial) plot"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"